The Statistical Analysis of Categorical Data

Overview

This book is about the analysis of categorical data with special emphasis on applications in economics, political science and the social sciences. The book gives a brief theoretical introduction to log-linear modeling of categorical data, then gives an up-to-date account of models and methods for the statistical analysis of categorical data, including recent developments in logistic regression models, correspondence analysis and latent structure analysis. Also treated are the RC association models brought to ...
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Overview

This book is about the analysis of categorical data with special emphasis on applications in economics, political science and the social sciences. The book gives a brief theoretical introduction to log-linear modeling of categorical data, then gives an up-to-date account of models and methods for the statistical analysis of categorical data, including recent developments in logistic regression models, correspondence analysis and latent structure analysis. Also treated are the RC association models brought to prominence in recent years by Leo Goodman. New statistical features like the use of association graphs, residuals and regression diagnostics are carefully explained, and the theory and methods are extensively illustrated by real-life data.
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Product Details

  • ISBN-13: 9783642788192
  • Publisher: Springer Berlin Heidelberg
  • Publication date: 7/31/2012
  • Edition description: 3rd ed. 1994. Softcover reprint of the original 3rd ed. 1994
  • Edition number: 3
  • Pages: 532
  • Product dimensions: 6.69 (w) x 9.61 (h) x 1.11 (d)

Table of Contents

1. Categorical Data.- 2. Preliminaries.- 2.1 Statistical models.- 2.2 Estimation.- 2.3 Testing statistical hypotheses.- 2.4 Checking the model.- 3. Statistical Inference.- 3.1 Log-linear models.- 3.2 The one-dimensional case.- 3.3 The multi-dimensional case.- 3.4 Testing composite hypotheses.- 3.5 The parametric multinomial distribution.- 3.6 Generalized linear models.- 3.7 Solution of likelihood equations.- 3.8 Exercises.- 4. Two-way Contingency Tables.- 4.1 Three models.- 4.2 The 2×2 table.- 4.3 The log-linear parameterization.- 4.4 The hypothesis of no interaction.- 4.5 Residual analysis.- 4.6 Exercises.- 5. Three-way Contingency Tables.- 5.1 The log-linear parameterization.- 5.2 Hypothesis in a three-way table.- 5.3 Hypothesis testing.- 5.4 Decomposition of the test statistic.- 5.5 Detection of model departures.- 5.6 Exercises.- 6. Multi-dimension Contingency Tables.- 6.1 The log-linear model.- 6.2 Interpretation of log-linear models.- 6.3 Search for a model.- 6.4 Diagnostics for model departures.- 6.5 Exercises.- 7. Incomplete Tables, Separability and Collapsibility.- 7.1 Incomplete tables.- 7.2 Two-way tables and quasi-independence.- 7.3 Higher order tables. Separability.- 7.4 Collapsibility.- 7.5 Exercises.- 8. The Logit Model.- 8.1 The logit-model with binary explanatory variables.- 8.2 The logit model with polytomous explanatory variables.- 8.3 Exercises.- 9. Logistic Regression Analysis.- 9.1 The logistic regression model.- 9.2 Regression diagnostics.- 9.3 Predictions.- 9.4 Polytomous response variables.- 9.5 Exercises.- 10. Models for the Interactions.- 10.1 Introduction.- 10.2 Symmetry models.- 10.3 Marginal homogeneity.- 10.4 Models for mobility tables.- 10.5 Association models.- 10.6 RC-association models.- 10.7 Log-linear association models.- 10.8 Exercises.- 11. Correspondence Analysis.- 11.1 Correspondence analysis for two-way tables.- 11.2 Correspondence analysis for multi-way tables.- 11.3 Comparison of models.- 11.4 Exercises.- 12. Latent Structure Analysis.- 12.1 Latent structure models.- 12.2 Latent class models.- 12.3 Continuous latent structure models.- 12.4 The EM-algorithm.- 12.5 Estimation in the latent class model.- 12.6 Estimation in the continuous latent structure model.- 12.7 Testing the goodness of fit.- 12.8 Diagnostics.- 12.9 Score models with varying discriminating powers.- 12.10 Comparison of latent structure models.- 12.11 Estimation of the latent variable.- 12.12 Exercises.- 13. Computer Programs.- References.- Author Index.- Examples with Data.
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